|
The Euler Equations of Compressible Fluid Flow
Author(s):
Demetrios
Christodoulou
Journal:
Bull. Amer. Math. Soc.
44
(2007),
581-602.
MSC (2000):
Primary 76L05, 76-03;
Secondary 01A50, 01A55, 01A60, 35L65, 35L67, 76N15
Posted:
June 18, 2007
Retrieve article in:
PDF DVI PostScript
References |
Similar articles |
Additional information
References:
-
- [Be]
- Bernoulli, D. Hydrodynamica, Argentorati (1738).
- [Bo]
- Boltzmann, L. ``Über die Bezeihung zwischen dem zweiten Hauptsatzes der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respective den Sätzen über das Wärmegleichgewicht'', Wien Ber. 76, 73 (1877).
- [Ch1]
- Christodoulou, D. The Formation of Shocks in 3-Dimensional Fluids, EMS Monographs in Mathematics, EMS Publishing House, 2007. MR 2284927
- [Ch2]
- Christodoulou, D. The Action Principle and Partial Differential Equations, Ann. Math. Stud. 146, Princeton University Press, 2000. MR 1739321 (2003a:58001)
- [C-K]
- Christodoulou, D., and Klainerman, S. The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series 41, Princeton University Press, 1993. MR 1316662 (95k:83006)
- [Cl1]
- Clausius, R. ``Über die bewegende Kraft der Wärme'', Annalen der Physik und Chemie 79, 368-397, 500-524 (1850).
- [Cl2]
- Clausius, R. ``Über verschiedene fü die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie'', Annalen der Physik und Chemie 125, 353-400 (1865).
- [DA]
- D'Alembert, J.-B. le R. ``Recherches sur la courbe que forme une corde tenduë mise en vibration'', Mém. Acad. Sci. Berlin 2, 214-219 (1849).
- [Ei]
- Einstein, A. ``Zur Electrodynamic bewegter Körper'', Annalem der Physik 17, 891-921 (1905).
- [Eu1]
- Euler, L. ``Principes generaux de l'etat d'equilibre des fluides'', Mémoires de l'Academie des Sciences de Berlin 11, 217-273 (1757).
- [Eu2]
- Euler, L. ``Principes generaux du mouvement des fluides'', Mémoires de l'Academie des Sciences de Berlin 11, 274-315 (1757).
- [Eu3]
- Euler, L. ``Continuation des recherrches sur la theorie du mouvement des fluides'', Mémoires de l'Academie des Sciences de Berlin 11, 316-361 (1757).
- [Eu4]
- Euler, L. ``Principia motus fluidorum'', Novi Commentarii Academiae Scientiarum Petropolitanae 6, 271-311 (1761).
- [Eu5]
- Euler, L. ``De motu fluidorum a diverso caloris gradu oriundo'', Novi Commentarii Academiae Scientiarum Petropolitanae 11, 232-267 (1767).
- [Eu6]
- Euler, L. ``Sectio secunda de principiis motus fluidorum'', Novi Commentarii Academiae Scientiarum Petropolitanae 14, 270-386 (1770).
- [Eu7]
- Euler, L. ``Sectio tertia de motu fluidorum lineari potissimum aquae'', Novi Commentarii Academiae Scientiarum Petropolitanae 15, 219-360 (1771).
- [Eu8]
- Euler, L. ``Sectio quarta de motu aeris in tubis'', Novi Commentarii Academiae Scientiarum Petropolitanae 16, 281-425 (1772).
- [F]
- Friedrichs, K.O. ``Symmetric hyperbolic linear differential equations'', Comm. Pure & Appl. Math. 7, 345-392 (1954). MR 0062932 (16:44c)
- [F-L]
- Friedrichs, K.O., and Lax, P.D. ``Systems of Conservation Equations with a Convex Extension'', Proc. Nat. Acad. Sci. USA 68, 1686-1688 (1971). MR 0285799 (44:3016)
- [Gl]
- Glimm, J. ``Solutions in the large for nonlinear hyperbolic systems of equations'', Comm. Pure & Appl. Math. 18, 697-715 (1965). MR 0194770 (33:2976)
- [He]
- Helmholtz, H. v. Über die Erhaltung der Kraft, G. Reimer, Berlin, 1847.
- [Hu]
- Hugoniot, H. ``Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits'', Journal de l'école polytechnique 58, 1-125 (1889).
- [J]
- John, F. ``Formation of singularities in one-dimensional non-linear wave propagation'', Comm. Pure & Appl. Math. 27, 377-405 (1974). MR 0369934 (51:6163)
- [Kr]
- Kruzhkov, S. N. ``First order quasilinear equations in several independent variables'', Math. USSR Sbornik 10, No. 2 (1970).
- [K-T]
- Keller, J.B. and Ting, L. ``Periodic vibrations of systems governed by nonlinear partial differential equations'', Comm. Pure & Appl. Math. 169, 371-420 (1966). MR 0205520 (34:5347)
- [La]
- Laplace, P. S. ``Sur la vitesse du son dans l'air et dans l'eau'', Ann. de Chim. et de Phys. iii, 238 (1816).
- [Ln]
- Landau, L.D. (1944). See Landau, L.D., and Lifschitz, E.M. Fluid Mechanics, 2nd edition, Oxford, Pergamon Press, 1987, pages 332-333. MR 961259 (89i:00006)
- [Lx1]
- Lax, P.D. ``Shock waves and entropy'', pp. 603-634 in Contributions to Nonlinear Functional Analysis, edited by E. Zarantonello, Academic Press, 1971. MR 0393870 (52:14677)
- [Lx2]
- Lax, P.D. ``Development of singularities of solutions of non-linear hyperbolic partial differential equations'', J. Math. Phys. 5, 611-613 (1964). MR 0165243 (29:2532)
- [Lx3]
- Lax, P.D. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, Regional Conf. Series in Appl. Math. 13, SIAM, 1973. MR 0350216 (50:2709)
- [Ma1]
- Majda, A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Appl. Math. Sci. 53, Springer-Verlag, 1984. MR 748308 (85e:35077)
- [Ma2]
- Majda, A. The Stability of Multi-Dimensional Shock Fronts - A New Problem for Linear Hyperbolic Equations, Mem. Amer. Math. Society 275, 1983.
- [Ma3]
- Majda, A. The Existence of Multi-Dimensional Shock Fronts, Mem. Amer. Math. Soc. 285, 1983. MR 699241 (85f:35139)
- [M-B]
- Majda, A., and Bertozzi, A. Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2002. MR 1867882 (2003a:76002)
- [Mi]
- Minkowski, H. ``Raum und Zeit'', Address at the 80th Assembly of German Natural Scientists and Physicians, Cologne (1908).
- [Mo]
- Morawetz, C. ``The decay of solutions of the exterior initial-boundary value problem for the wave equation'', Comm. Pure & Appl. Math. 14, 561-568 (1961). MR 0132908 (24:A2744)
- [N]
- Noether, E. ``Invariante Variationsprobleme'', Nach. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1918, 235-257 (1918).
- [Ra]
- Rankine, W.J.M. ``On the thermodynamic theory of waves of finite longitudinal disturbance'', Philosophical Transactions of the Royal Society of London 160, 277-288 (1870).
- [Ri]
- Riemann, B. ``Über die Fortpfanzung ebener Luftwellen von endlicher Schwingungswete'', Abhandlungen der Gesellshaft der Wissenshaften zu Göttingen, Mathematisch-physikalishe Klasse 8, 43 (1858-59).
- [S]
- Sideris, T. ``Formation of singularities in three-dimensional compressible fluids'', Commun. Math. Phys. 101, 475-85 (1985). MR 815196 (87d:35127)
- [Z-R]
- Zel'dovich, Y.B., and Raizer, Y.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phaenomena, New York, 1966, 1967, Chapter I, Section 19, and Chapter XI, Section 20.
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
76L05, 76-03, 01A50, 01A55, 01A60, 35L65, 35L67, 76N15
Retrieve articles in all Journals with MSC
(2000):
76L05, 76-03, 01A50, 01A55, 01A60, 35L65, 35L67, 76N15
Additional Information:
Demetrios
Christodoulou
Affiliation:
Departments of Mathematics and Physics, ETH-Zürich, ETH-Zentrum, 8092 Zürich, Switzerland
Email:
demetri@math.ethz.ch
DOI:
10.1090/S0273-0979-07-01181-0
PII:
S 0273-0979(07)01181-0
Received by editor(s):
May 15, 2007
Posted:
June 18, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
|